This is the best theological analysis of the Sincere Free Offer of the Gospel. Gib posits the grounds of the Sincere Free Offer in the Revealed Will of God, as opposed to the Decrees of God and the Extent of the Atonement. He distinguished and guards the doctrine from a General Atonement of the Arminians on the one hand, and relates it to Biblical Limited Atonement on the other hand. Gib was a mid-1700’s Scottish minister from the Seceder tradition.

For an all out Biblical and historic defense of the Sincere Free Offer of the Gospel, see the book by Rev. Silversides:

This is the most extensive work defending the Biblical view of the Sincere Free Offer of the Gospel. It also includes a valuable, extensive anthology of excerpts from historic, reformed writers demonstrating that the Sincere Free Offer of the Gospel has always been a regular part of reformed gospel preaching.